Turbine exhaust cases come in many different constructions. Sheet metal turbine exhaust cases typically comprise sheet metal inner and outer shrouds structurally interconnected by a plurality of circumferentially spaced-apart sheet metal hollow struts. The same sheet metal material is typically used for all the parts of the exhaust case to avoid thermal and structural mismatch, among other things. It is desirable for the outer shroud and the inner shroud to generally have the same stiffness to avoid shroud deformation in response to the thermal growth of the struts. These thermal and stress constraints together with the need for lightweight materials have limited the choices available in the construction of sheet metal turbine exhaust cases.